When True, generates a symmetric window, for use in filter design.
When False, generates a periodic window, for use in spectral analysis.

Returns :

w : ndarray

The window, with the maximum value normalized to 1 (though the value 1
does not appear if the number of samples is even and sym is True).

Notes

The Kaiser window is defined as

with

where is the modified zeroth-order Bessel function.

The Kaiser was named for Jim Kaiser, who discovered a simple approximation
to the DPSS window based on Bessel functions.
The Kaiser window is a very good approximation to the Digital Prolate
Spheroidal Sequence, or Slepian window, which is the transform which
maximizes the energy in the main lobe of the window relative to total
energy.

The Kaiser can approximate many other windows by varying the beta
parameter.

beta

Window shape

0

Rectangular

5

Similar to a Hamming

6

Similar to a Hann

8.6

Similar to a Blackman

A beta value of 14 is probably a good starting point. Note that as beta
gets large, the window narrows, and so the number of samples needs to be
large enough to sample the increasingly narrow spike, otherwise NaNs will
get returned.

Most references to the Kaiser window come from the signal processing
literature, where it is used as one of many windowing functions for
smoothing values. It is also known as an apodization (which means
“removing the foot”, i.e. smoothing discontinuities at the beginning
and end of the sampled signal) or tapering function.